Hedge Swap

History:

To raise new capital, one japanese bank with AAA rating, issues an exotic bond for one of his investors and wants to fully eliminate exotic risk.

For this the bank contacts HSBC to buy a hedge by entering into cross currency callable swaption with the same exotic coupons as the bond.

The exotic coupons are fully hedged by definition of contract. But our bank and HSBC, using different interest rates curve, have different estimatation of early exercise probabilities.

The bank absolutely wants to kill the bond if HSBC kill the hedge swap in order to not be left with exotic coupons face to investor.

Why the interest rates curve are different?

The difference between HSBC and AAA bank curves comes from two sources:

1. Incorporated credit risk in curves (HSBC and our AAA bank have different credit risks)
2. Collateral. While exotic swaption is collateralized, callable exotic bond is not.

Idea:

Two products are priced with one of the stochastic diffusion type models.

The idea is to integrate hedge swap kill probabilities into callable bond.

1. diffuse the model (MC) or build the grid (PDE) for callable bond pricing
2. price hedge swap on the same diffusion/grid using hedge swap pricing curves
3. estimate hedge swap kill probabilities
4. price the callable bond with hedge swap probabilities using bond pricing curves

Project: implementation 

FAQ

Why bank AAA dosn't sign the same callable bond with HSBC?

Npv has changed, which one is better?

Old npv is just price of callable bond as it is. New npv incorporates the fact that the bond is always callable once the hedge swap is.

Can we have an arbitrage?

No. It's structured product, no liquidity